1. Field of the Invention The present invention relates generally to a method of and an apparatus for measuring minute distances or dimensions and, more specifically, it relates to a method of and an apparatus for measuring the distance between two surfaces of a semiconductor wafer. Measurement is performed in a non-destructive and non-contact manner.
2. Description of the Prior Art
In a dynamic RAM (random access memory) having large storage capacity, trench capacitors are widely employed in order to improve the degree of integration. FIG. 1 is a cross sectional view showing one memory cell of a dynamic RAM having a trench capacitor. Referring to FIG. 1, the dynamic RAM comprises a semiconductor substrate 101 of, for example p-type, having a trench 102, n-type impurity diffused layers 103 and 104 formed on a main surface of the semiconductor substrate 101, a gate electrode 105 formed on a region sandwiched by the n-type impurity diffused layers 103 and 104 with an insulating film interposed therebetween, an n-type impurity diffused layer 106 formed around the trench 102 and connected to the n-type impurity diffused layer 104 and a capacitor electrode 107 formed of polycrystalline silicon formed on the n-type impurity diffused layer 106 with an insulating film interposed therebetween. The n-type impurity diffused layer 106, the capacitor electrode 107 and the insulating film interposed therebetween constitute a trench capacitor. The width W and the depth D (see FIG. 1) of the trench in a highly integrated memory cell are about 1 .mu.m and several .mu.m, respectively. The capacity of the trench capacitor is a function of the depth of the trench. Therefore, in order to govern the characteristic value of a semiconductor memory device of this type, the depth of the trench must be precisely measured in a non-destructive and non-contact manner during manufacture.
Examples of conventional methods for measuring
the depth of a trench in a non-destructive or non-contact manner include: the wavelength spectral method and the interference spectral method.
In both of these methods, a microlevel difference at a step portion of a sample surface is measured by detecting spectrum of light reflected from the sample's surface, as will be described later. The former method employs a means for detecting an interference effect.
The detecting means is a spectrophotometry means comprising a spectroscope such as a prism, diffraction grating, or the like. The latter method, employs a detecting means which spectrophotometry is a means comprising an interferometer.
FIG. 2 illustrates the conventional measuring methods.
A micro-trench 36 for forming a trench capacitor, for example, is formed on a surface 16A of a sample 16 of a silicon wafer, for example. Visible white light L.sub.1, for example, impinges upon the surface 16a in a direction which is substantially perpendicular to the sample surface 16A.
The visible white light L.sub.1 is reflected by a flat surface (upper portion) of the sample surface 16A and from the bottom of the trench 36 (lower portion). Consequently, a phase difference corresponding to the depth of the trench is generated between the light L.sub.21 reflected from the flat surface of the sample surface 16A and the light L.sub.22 reflected from the bottom of the trench 36. The amplitude of the reflected light varies depending on the wavelength, of the light thereby generating an interferenced light.
The results of measuring the spectral intensity of such reflected light L.sub.2 is shown FIG. 3A. The results shown in FIG. 3A occur when the proportion of the area occupied by the trench in the measured region of the surface is relatively large. As is apparent from FIG. 3A, the intensity distribution of the spectrum changes as a function of to the wavelength .lambda.. The distance H between the wave crests of the change corresponds to the depth D of the trench 36.
The reason for this will be briefly described in the following.
FIG. 4 schematically illustrates a principle useful in measuring the thickness of a thin film. Referring to FIG. 4, A denotes an air layer, B denotes a single layer film and C denotes a substrate, having reflectances of n.sub.2, n.sub.1 and n.sub.0, respectively. Lines with arrows show the direction of passing light. Although as a practical matter the light does not always impinge vertically, the reflectance .vertline.R1.vertline..sup.2 of the light can be represented by the following equation,
in which it is assumed that the light impinges only vertically: EQU .vertline.R1.vertline..sup.2 =1-4n.sub.0 n.sub.1.sup.2 n.sub.2 /{n.sub.1.sup.2 (n.sub.0 +n.sub.1).sup.2 -(n.sub.1.sup.2 -n.sub.2.sup.2).(n.sub.0.sup.2 -n.sub.1.sup.2) sin .sup.2 .delta..sub.1 /2}(1)
where
.delta..sub.1 =4.pi.n.sub.1 d.sub.1 /.lambda.
d.sub.1 =thickness of the film (see FIG. 4)
.lambda.=wavelength
(the above equation is disclosed in, for example, Oyokogaku Gairon (Introduction to Applied Optics) by Tsutusi et al., Kinpara Shuppan, pp. 217 to 218, 1969).
The value .vertline.R.sub.1 (.lambda.).vertline. shown in the above equation (1) is a function of sin.sup.2 .delta./2. Therefore, the wave crests and wave troughs of the .vertline.R.sub.1 (.lambda.).vertline. curve are repeated periodically by .delta..sub.1 =4.pi.n.sub.1 (.lambda.)d.sub.1 /.lambda.=2.pi. from the qualitative point of view. If the difference between the path taken by light reflected from the bottom of the trench and the path taken by light reflected from the surface of the wafer is an even number times the wavelength of the light, then the amplitude of the light is large. However, if the difference is an odd number times the wavelength of the light, the amplitude of the light is small. Therefore, assuming that the depth of the trench is uniform, the number of wave crests representing .vertline.R.sub.1 (.lambda.).vertline. is dense if the wavelength is short, while the number is less dense if the wavelength is long.
An example of the curve is shown in FIG. 5. FIG. 5 is a graph in which the x axis represents the wavelength while the y axis represents .vertline.R.sub.1 (.lambda.).vertline.. In FIG. 5, the following equations are satisfied: ##EQU1##
x: number of repetitions of wave crests and wave troughs
m: integer
n.sub.1 (.lambda..sub.s): reflectance of the film at wavelength .lambda..sub.s
n.sub.1 (.lambda..sub.2): reflectance of the film at wavelength .lambda..sub.2
d.sub.1 : thickness of the film
Therefore, the thickness of the film can be measured from the number of peaks x in a certain wavelength range of and from the reflectance of the film to be measured. By applying this method, the depth of a trench can be measured when the thickness of the film is replaced with the depth of the trench. Thus, FIG. 5 corresponds to FIGS. 3A and 3B.
Since a trench formed on a sample such as a silicon wafer is extremely narrow as shown in FIG. 1, the total of the bottom area of trenches is in most cases less than 10% of the area of the region to be measured. If such sample is measured by a conventional method, a large portion of the reflected light will be regularly reflected from a flat portion of the sample surface 16A and not from the trench. Therefore, the proportion of the interferenced light derived from the microlevel difference to the total reflected light becomes extremely small. Consequently, when the light reflected from such sample surface is spectrally analyzed, the average intensity (the average of intensity at each wavelength) is high, and the amplitude (the intensity difference between a wave crest and a wave trough) is small as shown in FIG. 3B. In other words, all of the signals provided have a small amplitude relative to the average intensity. (This comparison is hereinafter referred to as "contrast"). Therefore, due to the low contrast the depth of the trench cannot be precisely measured. The intensity of the spectrum shown in FIG. 3A (in which the trench occupies a relatively large area) is lower than that of the spectrum shown in FIG. 3B (in which the trench occupies a relatively small area). The reason for this is that a relatively large amount of light is diffracted from the trench and the amount of light which enters the optical system (which converges the light reflected from the surface sample) is small. In order to solve the above described problems, the following method has been proposed.
A portion of a substrate surface which has an actual pattern (for example a pattern used as a trench capacitor) is replaced with a test portion which has a trench pattern in which the trench is proportionately large. The test pattern is measured by the above described method. The depth of the trench in the actual pattern is then estimated based on the result. However, this method comprises the following problems. Namely, since a test pattern which is not used as an actual device is formed on the silicon wafer surface, the total surface area of the wafer is unnecessarily increased. Thus, this method is particularly undesirable for forming a highly integrated semiconductor device. In addition, if the areas occupied by the trench in the test pattern and in the actual pattern are not accurately proportional to each other, the depth of
the trenches in both patterns are liable to differ from each other in the manufacturing process. Consequently, even if the depth of the trench in the test pattern is precisely measured, the depth of the trench in the actual pattern cannot always be precisely measured based on the result of the measurement of the test pattern.